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Answer :
To find out how many frozen dinners can be bought in 16 years if the purchasing power decreases by 5% each year due to inflation, follow these steps:
1. Understand the Concept of Inflation: Inflation leads to a decrease in purchasing power, meaning that over time, you can buy less with the same amount of money. In this problem, inflation is reducing purchasing power by 5% per year.
2. Initial Quantity: Start with the initial number of frozen dinners you can buy, which is 940.
3. Calculate the Annual Decrease: Since the purchasing power decreases by 5% each year, it retains 95% of its previous year's power. You can express this as retaining 0.95 (which is 1 - 0.05) of its purchasing power each year.
4. Calculate the Purchasing Power Over 16 Years: To find out how much purchasing power remains after 16 years, multiply the initial purchasing power by 0.95 for each of the 16 years. This is expressed as:
[tex]\[
\text{Purchasing Power} = 940 \times (0.95)^{16}
\][/tex]
5. Compute the Result: This calculation will give you the number of frozen dinners you can buy in 16 years. When you do the math, you find that the purchasing power of your money buys approximately 413.72 frozen dinners.
6. Round to the Nearest Whole Number: Since you can't buy a fraction of a frozen dinner, round 413.72 to the nearest whole number, which is 414.
Therefore, in 16 years, you will be able to buy approximately 414 frozen dinners.
1. Understand the Concept of Inflation: Inflation leads to a decrease in purchasing power, meaning that over time, you can buy less with the same amount of money. In this problem, inflation is reducing purchasing power by 5% per year.
2. Initial Quantity: Start with the initial number of frozen dinners you can buy, which is 940.
3. Calculate the Annual Decrease: Since the purchasing power decreases by 5% each year, it retains 95% of its previous year's power. You can express this as retaining 0.95 (which is 1 - 0.05) of its purchasing power each year.
4. Calculate the Purchasing Power Over 16 Years: To find out how much purchasing power remains after 16 years, multiply the initial purchasing power by 0.95 for each of the 16 years. This is expressed as:
[tex]\[
\text{Purchasing Power} = 940 \times (0.95)^{16}
\][/tex]
5. Compute the Result: This calculation will give you the number of frozen dinners you can buy in 16 years. When you do the math, you find that the purchasing power of your money buys approximately 413.72 frozen dinners.
6. Round to the Nearest Whole Number: Since you can't buy a fraction of a frozen dinner, round 413.72 to the nearest whole number, which is 414.
Therefore, in 16 years, you will be able to buy approximately 414 frozen dinners.
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